Bayesian Meta-Analysis for Binary Data and Prior Distribution on Models

Miguel-Angel Negrín-Hernández, María Martel-Escobar and Francisco-José Vázquez-Polo
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Miguel-Angel Negrín-Hernández: Department of Quantitative Methods & TiDES Institute, University of Las Palmas de Gran Canaria, E-35017 Las Palmas de Gran Canaria, Spain
María Martel-Escobar: Department of Quantitative Methods & TiDES Institute, University of Las Palmas de Gran Canaria, E-35017 Las Palmas de Gran Canaria, Spain
Francisco-José Vázquez-Polo: Department of Quantitative Methods & TiDES Institute, University of Las Palmas de Gran Canaria, E-35017 Las Palmas de Gran Canaria, Spain

IJERPH, 2021, vol. 18, issue 2, 1-18

Abstract: In meta-analysis, the structure of the between-sample heterogeneity plays a crucial role in estimating the meta-parameter. A Bayesian meta-analysis for binary data has recently been proposed that measures this heterogeneity by clustering the samples and then determining the posterior probability of the cluster models through model selection. The meta-parameter is then estimated using Bayesian model averaging techniques. Although an objective Bayesian meta-analysis is proposed for each type of heterogeneity, we concentrate the attention of this paper on priors over the models. We consider four alternative priors which are motivated by reasonable but different assumptions. A frequentist validation with simulated data has been carried out to analyze the properties of each prior distribution for a set of different number of studies and sample sizes. The results show the importance of choosing an adequate model prior as the posterior probabilities for the models are very sensitive to it. The hierarchical Poisson prior and the hierarchical uniform prior show a good performance when the real model is the homogeneity, or when the sample sizes are high enough. However, the uniform prior can detect the true model when it is an intermediate model (neither homogeneity nor heterogeneity) even for small sample sizes and few studies. An illustrative example with real data is also given, showing the sensitivity of the estimation of the meta-parameter to the model prior.

Keywords: bayesian meta-analysis; clustering; binary data; priors; frequentist validation (search for similar items in EconPapers)
JEL-codes: I I1 I3 Q Q5 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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